# SL(2,3) in SL(2,5)

From Groupprops

This article is about a particular subgroup in a group, up to equivalence of subgroups (i.e., an isomorphism of groups that induces the corresponding isomorphism of subgroups). The subgroup is (up to isomorphism) special linear group:SL(2,3) and the group is (up to isomorphism) special linear group:SL(2,5) (see subgroup structure of special linear group:SL(2,5)).VIEW: Group-subgroup pairs with the same subgroup part | Group-subgroup pairs with the same group part | All pages on particular subgroups in groups

## Definition

The group is taken as special linear group:SL(2,5): the special linear group of degree two over field:F5.

The subgroup is taken as a representative of the unique conjugacy class of subgroups of order 24. (The conjugacy class contains 5 subgroups).

This subgroup can be obtained explicitly using the quaternionic representation of special linear group:SL(2,3) over field:F5 (see also linear representation theory of special linear group:SL(2,3)).

## Arithmetic functions

Function | Value | Explanation |
---|---|---|

order of the whole group | 120 | . See special linear group:SL(2,5) for more. |

order of the subgroup | 24 | . See special linear group:SL(2,3) for more. |

index of the subgroup | 5 | |

size of conjugacy class of subgroup | 5 | |

number of conjugacy classes in automorphism class | 1 |